Question

A water trough is m long and a cross-section has the shape of an isosceles trapezoid that is cm wide at the bottom, cm wide at the top, and has height cm. If the trough is being filled with water at the rate of , how fast is the water level rising when the water is cm deep

Answer 1

The rate of water level rising when the water is 30 cm deep will be 1/30 m/min.

What is volume?

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.

The complete question is;

"A water trough is 10m long and has a cross-section which is the shape of an isosceles trapezoid

that is 30cm wide at the bottom, 80cm wide at the top, and has a height of 50cm. If the trough is being filled with water at the rate of 0.2 m3/min, how fast is the water level rising when the water is 30cm deep?"

b1 is the width of the water at a height at the bottom

b2 is the width of the water at the height at the top

The length of the trapezoid is L

The volume of the trapezoid is found as;

$\rm V = 0.5(b_1 + b_2)hL$

The breadth rises by 1 as the height does, therefore which implies

$\rm \frac{dh}{dt} =\frac{dw}{dt}$

The water's breadth at the combined height is [0.3 + h]

$\rm V = 5h(0.3 +(0.3 + h))\\\\ V = 3h + 5h^2$

After differentiation we get;

$\rm \frac{dv }{dt} =3 \frac{dh}{dt} +10 h \frac{dh}{dt} \\\\\ \frac{ \frac{dv }{dt}}{3+10h}=\frac{dh}{dt} \\\\\ \frac{dv }{dt}= 0.2 \\\\\ h = 0.3 \\\\ \frac{dh}{dt} = \frac{1}{30} m/min$

Hence the rate of water level rising when the water is 30 cm deep will be 1/30 m/min.

To learn more about the volume, refer to brainly.com/question/1578538.

#SPJ1